Strong-coupling Properties of a $p$-wave Interacting Fermi Gas on the Viewpoint of Specific Heat at Constant Volume

TL;DR

This paper theoretically analyzes the specific heat of a $p$-wave interacting Fermi gas across different coupling regimes, revealing fluctuation effects near the superfluid transition and classifying the normal state phases.

Contribution

It applies strong-coupling theory to elucidate how $C_V$ varies with temperature and interaction strength in a $p$-wave Fermi gas, providing a phase classification of the normal state.

Findings

$C_V$ is enhanced by pairing fluctuations near $T_c$ in weak coupling.

In strong coupling, $C_V$ reflects a Bose gas of $p$-wave molecules.

Normal state classified into Fermi gas, molecular Bose gas, and fluctuation-dominated regions.

Abstract

We theoretically investigate the specific heat $C_V$ at constant volume in the normal state of a $p$-wave interacting Fermi gas. Including fluctuations in the $p$-wave Cooper channel within the framework of the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink, we clarify how $C_V$ as a function of temperature varies, as one moves from the weak-coupling regime to the strong-coupling limit. In the weak-coupling regime, $C_V$ is shown to be enhanced by $p$-wave pairing fluctuations, near the superfluid phase transition temperature $T_{\rm c}$. Similar enhancement of $C_V(T\simeq T_{\rm c})$ is also obtained in the strong-coupling regime, which, however, reflects that system is close an ideal Bose gas of $p$-wave two-body bound molecules. Using these results, we classify the normal state into (1) the normal Fermi gas regime, (2) the $p$-wave molecular Bose gas regime, and (3) the region between the two, where $p$-wave pairing fluctuations are dominant. Since the current experiments can only access the normal phase of a $p$-wave interacting Fermi gas, our results would be useful for experiments to understand strong-coupling properties of this Fermi system above $T_{\rm c}$.